The Brexit Secretary is set to return to Brussels next week for talks with the EU's chief negotiator Michel Barnier.
At the heart of the problem is ensuring there is no hard border between Northern Ireland and the Irish Republic, which both Britain and the European Union have committed to.
And he said Mrs May's insistence that the arrangement must be time-limited meant that it could not be regarded as a true backstop, providing a fallback option if the UK's preferred permanent solution could not be agreed.
Ministers are also concerned as it does not state that Britain will be able to unilaterally decide when the backstop should end, which had been one of their key demands, the Telegraph reported. The UK would also be bound by some parts of the EU's Common Commercial Policy (CCP), meaning it would be required to apply the EU's common external tariff (CET) and Union Customs Code at the UK border.
A new campaign for a second referendum on the U.K.'s exit from the European Union, which is allegedly partly sponsored by US billionaire George Soros, has been launched in London on Friday. Just as "Brexit means Brexit", paragraph 49 makes clear that "a backstop means a backstop", that is to say something that will come into operation should no other solution be found.
Theresa May has avoided a potentially devastating cabinet resignation after striking a last-minute deal with David Davis over plans to prevent a hard border in Ireland after Brexit.
Brussels has said there needs to be progress on a solution by the June 28-29 European Union summit to prevent the return of border checks between European Union member Ireland and the British province of Northern Ireland.
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"We are no closer to knowing the relationship Britain is going to have (with the EU)", said Jane Foley, a currencies strategist at Rabobank, adding that many investors were waiting it out in the meantime.
She rejected arguments that the 2016 result was "etched in stone" and should not be questioned, saying: "The will of the people is changing. the 48% is now over 50% and rising".
But the government is struggling to find a way to fulfil this commitment while sticking to its plan to leave the EU's single market and customs union after Brexit.
"Our backstop can not be extended to the whole U.K.", Barnier said.
Mr Johnson was heard warning of a Brexit meltdown and said the United Kingdom could end up in the customs union and to a large extent still in the single market in the recording obtained by BuzzFeed News. We believe this is the right thing to do so that everyone's voice can be heard.
On Thursday, Theresa May was forced to say she "expects" there to be a cut-off date after Brexit Secretary David Davis allegedly threatened to resign.
The idea of the backstop is controversial with eurosceptics, who fear it will keep Britain tied to the EU's rules for years after it leaves the bloc on March 29, 2019.
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